erik winfree, furong liu, lisa a. wenzler and nadrian c. seeman- design and self-assembly of...

Nature © Macmillan Publishers Ltd 1998

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NATURE | VOL 394 | 6 AUGUST 1998 539

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Design and self-assembly oftwo-dimensional DNA crystalsErik Winfree*, Furong Liu†, Lisa A. Wenzler† & Nadrian C. Seeman†

* Computation and Neural Systems, California Institute of Technology, Pasadena, California 91125, USA† Department of Chemistry, New York University, New York, New York 10003, USA

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Molecular self-assembly presents a ‘bottom-up’ approach to the fabrication of objects specified with nanometreprecision. DNA molecular structures and intermolecular interactions are particularly amenable to the design andsynthesis of complex molecular objects.We report the design and observation of two-dimensional crystalline formsofDNA that self-assemble from synthetic DNA double-crossover molecules. Intermolecular interactions between thestructural units are programmed by the design of ‘sticky ends’ that associate according to Watson–Crickcomplementarity, enabling us to create specific periodic patterns on the nanometre scale. Thepatterned crystals havebeen visualized by atomic force microscopy.

Control of the detailed structure of matter on the finest possiblescale is a major goal of chemistry, materials science and nanotech-nology. This goal may be approached in two steps: first, theconstruction of individual molecules through synthetic chemistry;and second, the arrangement of molecular building blocks intolarger structures. The simplest arrangements of molecular units, intwo or three dimensions, are periodic—a crystal. Design componentsfor crystals must have definable intermolecular interactions and mustbe rigid enough to prevent the formation of ill-defined aggregates1.Branched DNA molecules with sticky ends are promising for macro-molecular crystal design2 because their intermolecular interactionscan be programmed through sticky ends3 that associate to produceB-form DNA4; however, studies of three- and four-arm junctionsreveal that the angles flanking their branchpoints are flexible5,6.

The need for a rigid design component with predictable andcontrollable interactions has led to the utilization of the antiparallelDNA double-crossover motif 7 for this purpose. Double-crossover(DX) molecules are analogues of intermediates in meiosis8 thatconsist of two side-by-side double-stranded helices linked at twocrossover junctions. Antiparallel DX molecules have a rigidity that islacking in conventional branched junctions, indicating that theymight be suitable for use in the assembly of periodic matter9.

These findings stimulated a theoretical proposal to use two-dimensional (2-D) lattices of DX molecules10 for DNA-based compu-tation11. In the mathematical theory of tilings12, rectangular tiles withprogrammable interactions, known as Wang tiles, can be designed sothat their assembly must mimic the operation of a chosen TuringMachine13. DX molecules acting as molecular Wang tiles could self-assemble to perform desired computations10,14,15. Consequently, theability to create 2-D lattices of DX molecules assumes additionalinterest as a step towards the design of molecular algorithms.

Here we report the assembly, from DX molecules, of three 2-Dlattices with two distinct topologies. The DX molecules,,2 3 4 3 13 or 2 3 4 3 16 nm in size, self-assemble in solutionto form single-domain crystals as large as 2 3 8 mm with uniformthickness between 1 and 2 nm, as visualized by atomic forcemicroscopy16 (AFM). By incorporating a DNA hairpin into a DXmolecule to serve as a topographic label, we have produced stripesabove the surface at intervals of 25, 32 and 64 nm. Two-componentlattices have been assembled with a stripe every other unit; byprogramming sticky-ended associations differently, four-componentlattices have been produced with a strip every fourth unit. Thisobservation demonstrates that it is possible to create specific lattices

with programmable structures and features on a nanometre scale.

Design of DNA crystalOur approach to two-dimensional crystal design is derived from themathematical theory of tiling10,12. The desired lattice is specified by aset of Wang tiles with coloured edges; the Wang tiles may be placednext to each other only if their edges are identically coloured wherethey touch (Fig. 1a). Our goal is to design synthetic molecular unitscorresponding to these tiles, such that they will self-assemble into acrystal that obeys the colouring conditions. As an initial demonstra-tion of molecular Wang tiles, we have chosen the simplest non-trivialset of tiles: two tiles, A and B, which make a striped lattice (Fig. 1a,left). We also demonstrate a set of four tiles that produce a stripedlattice with a greater period (Fig. 1a, right). Translated into molecularterms, we obtain DX systems that self-assemble in solution intotwo-dimensional crystals with a well defined subunit structure.

The antiparallel DX motif 7 consists of two juxtaposed immobile4-arm junctions2 arranged so that at each junction the non-cross-over strands are antiparallel to each other. There are five distinct DXmotifs, but only two are stable in small molecules7: these are calledDAO (double crossover, antiparallel, odd spacing) and DAE (doublecrossover, antiparallel, even spacing). The design depends criticallyupon the twist of the B-form DNA double helix, in which a full turntakes place in ,10.5 base pairs17,18. DAO molecules have an oddnumber of half-turns (e.g. 3 half-turns is ,16 base pairs) betweenthe crossover points, whereas DAE molecules have an even numberof half-turns (for example, 4 half-turns is ,21 base pairs). Com-puter models of the DX molecules used in this study are shown inFig. 1b. The DAO molecules consist of four strands of DNA, each ofwhich participates in both helices. The DAE molecules consist ofthree strands that participate in both helices (yellow, light blue,green), and two strands that do not cross over (red, dark blue). Eachcorner of each DX unit has a single-stranded sticky end with aunique sequence; specific association of DX units is controlled bychoosing sticky ends with Watson–Crick complementarity.

To ensure that the component strands form the desired com-plexes, strand sequences must be designed carefully so that alter-native associations and conformations are unlikely. Therefore wemust solve the ‘negative design problem’19–21 for DNA: findsequences that maximize the free energy difference between thedesired conformation and all other possible conformations. We usethe heuristic principle of sequence symmetry minimization2,19 tominimize the length and number of unintentional Watson–Crick


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complementary subsequences. In each DX molecule’s sequences,there are no 6-base subsequences complementary to other 6-basesubsequences except as required by the design, and spurious 5-basecomplementarity is rare. Thus it is expected that during self-assembly, the DNA strands spend little time in undesired associa-tions and form DX units with high yield.

DX units can be designed that will fit together into a two-dimensional crystalline lattice. Here we use either two or fourdistinct unit types (Fig. 1a) to produce striped lattices. We usetwo separate systems to implement the two-unit lattice, one con-sisting of two DAO units, the other consisting of two DAE units. The

lattices produced by these systems are called DAO-E and DAE-O,respectively, to indicate the number of half-turns between crossoverpoints on adjacent units; their distinct topologies are shown in Fig.1c. Covalently joining adjacent nucleotides at nicks in the lattice, bychemical or enzymatic ligation, would result in a ‘woven fabric’ ofDNA strands. Ligation of the DAO-E design produces four distinctstrand types, each of which continues infinitely in the verticaldirection (here, the terms ‘vertical’ and ‘horizontal’ will always beas in Fig. 1c). The DAE-O design involves two small nicked circularstrands in addition to four infinite strands, two of which extendhorizontally and two of which extend vertically. The DAO-E

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540 NATURE | VOL 394 | 6 AUGUST 1998

Figure 1 Design of DX molecular structure and arrangement into 2-D lattices. a,

The logical structure for 2-D lattices consisting of two units and four units. In the

two-unit design, type A units have four coloured edge regions, each of which

match exactly one coloured region of the adjacent type B units. Similarly, in the

four-unit design, the edge colours are chosen uniquely to define the desired

relations between neighbouring tiles. Note that rotations and reflections of Wang

tiles aredisallowed; anequivalent restriction could also be obtained byusingnon-

rectangular tiles or more complex patterns of colours. b, Model structures for

DAO andDAE typeAunits. Each component oligonucleotide is shown in a unique

colour. The crossover points arecircled.Complete base stackingat the crossover

points is assumed. Computer models showing every nucleotide (nt) were

generated using NAMOT2 (ref. 39). c, The lattice topologies produced by the DAO

and DAE units. Each DX unit is highlighted by a grey rectangle. A unique colour is

chosen for each strand type which would be formed after covalent ligation of

units. Arrowheads indicate the 39 ends of strands. Black ellipses indicate dyad

symmetry axes perpendicular to the plane; black arrows indicate dyad axes in the

plane (full arrowhead) or screw axes (half arrowhead). The symmetries of the

DAO-E and DAE-O lattices are those corresponding to the layer groups40 P2122

and P21212 respectively. The boundaries of the DAE-O units are not designed to

coincide with the vertical symmetry elements. d, The actual sequences used in

the reported experiments (see Methods for several exceptions). The schematics

accurately report primary and secondary structure—oligonucleotide sequence

and paired bases—but are not geometrically or topologically faithful because they

do not show the double-helical twist. Both type B and type B areshown, indicating

where the hairpin sequences are inserted. Note that for each type—A, B, and B—

there is both a DAO unit and a DAE unit.


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design has the advantage of using simple 4-strand DX units,whereas in the DAE-O design, the horizontal and vertical strandscan serve as reporters for the extent of self-assembly if the moleculesare ligated and analysed by gel electrophoresis. We have investi-gated both the DAO-E and DAE-O systems in parallel to showthat the same principles of self-assembly govern both systems.Therefore, except where noted, our discussion will apply to bothsystems.

Control of self-assembly to yield the 2-D lattice is obtained by twodesign criteria. First, the sticky-end sequences for each desiredcontact are unique; this ensures that the orientations and adjacencyrelations of the DX units comply exactly with the design in Fig. 1a.Sticky ends are lengths 5 and 6 for the DAO-E and DAE-O designsrespectively, so that each correct contact contributes ,8 or14 kcal mol−1 to the free energy of association at 25 8C, accordingto a nearest-neighbour model22. Second, the lengths of the DX armsand sticky ends, and thus the separations between crossover points,respect as closely as possible the natural twist of the B-form DNAdouble helix; thus adjacent DX molecules are effectively coupled bytorsional springs whose equilibrium positions have been designedto keep the adjacent DX molecules coplanar. For example, a linearrather than planar polymer could result if each unit makes twosticky-end bonds to each neighbouring unit, but this would requireovertwisting, undertwisting, or bending of the double helix, andthus is discouraged by our design.

Figure 1d shows the DX units and sequences used in ourexperiments, except as noted in Methods. In each system, thereare two fundamental DX units, called A and B, and, additionally, analternative form B that contains two hairpin-terminated bulged 3-arm junctions (similar to the DX þ J motif9). On the basis of studiesof bulged 3-arm junctions23, we expect that in each unit, one hairpinwill point up and out of the plane of the DX crystal, while the otherhairpin will point down and into the plane, without significantlyaffecting the rigidity of the molecule9. The B units will replace the Bunits and serve as contrast agents for AFM imaging, because theirincreased height can be measured directly. Related sequences wereused for the four-unit lattice ABCD and for studies involving goldlabelling or alternative placements of the hairpins.

Characterization by gel electrophoresisA prerequisite for lattice self-assembly is the formation of the DXunits from their component strands. A thorough investigation ofthis issue was done for the original studies of DX7; that the newdesigns also behave well constitutes further validation of theantiparallel DX motif. Because the sticky ends of A units haveaffinity only for sticky ends of B units, and not for themselves,neither A nor B alone in solution can assemble into a lattice. Thusthe formation of isolated DX units can be monitored easily by non-denaturing gel electrophoresis, as described previously7, and morethan 95% of the material is seen in the expected band.

Solutions containing A units and B units can be mixed andannealed to form AB lattices. Enzymatic ligation of these latticeswith T4 DNA ligase should produce long covalent DNA strands.The nicks, where strands from adjacent DX units abut, are all on theupper or lower surface of the lattice, where they are accessible to theenzyme. The long strands can serve as reporters of successful latticeformation; shorter strands report either the presence of smallaggregates or an occasional failure to ligate within the lattice. Inthe DAO-E design there are four vertical reporter strands, whereasin the DAE-O design there are two horizontal and two verticalreporter strands. All four reporter strands extend for more than 30repeats when visualized by denaturing polyacrylamide gel electro-phoresis (PAGE) (Fig. 2; data for DAO-E not shown). Longerstrands co-migrate on this gel, so we cannot determine the fullextent of polymerization. These results suggest that the lattice is agood substrate for T4 DNA ligase, and that the lattice can form withmore than 30 3 30 units. However, unintended associations or side

reactions could lead to similar distributions of strand lengths afterligation. Direct physical observation is necessary to confirm latticeassembly.

AFM imagingWe have used atomic force microscopy16 to demonstrate unequi-vocally the formation of 2-D lattices. A and B units are annealedseparately, then combined and annealed together to form ABlattices. The resulting solution is deposited for adsorption on anatomically flat mica surface, and then imaged under isopropanol bycontact mode AFM24. The solution is not treated with DNA ligase,and thus the lattices are held together only by noncovalent interac-tions (for example, hydrogen bonds and base stacking). Thisprotocol ensures that the solution contains no protein contami-nants and demonstrates that ligase activity is not necessary for theself-assembly process. Negative controls of buffer alone and of A orB alone show no aggregates larger than 20 nm (data not shown). Inseparate experiments, A and B DAO units were modified by theremoval of two sticky ends from each unit (for example, all yellowand red sticky ends in Fig. 1d); when the modified A and B unitswere annealed together, we observed only linear and branched struc-tures with apparent widths typically less than 10 nm (data not shown),providing additional negative controls. However, the unmodified AB

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Figure 2 Autoradiogram of a 4% denaturing polyacrylamide gel showing the

product after assembly of 2-D lattice DAE-O (AB), ligation to form long covalent

strands, and denaturing to separate the strands. Lane 1 contains a ladder or

markers at 100-base intervals. In the remaining lanes, a different strand from unitB

is labelled: lanes 2 and 3 correspond to red strands (Fig.1c, right), lanes 4 and 5

are green strands, lane 6 and 7 are blue strands, and lanes 8 and 9 are yellow

strands. Escherichia coli exonucleases I and III were added to the material in the

odd-numbered lanes to degrade single-stranded species, indicating that no

circular products were formed. As red strands are lengths 46 and 48, in lane 2 we

see bands at lengths 94k and 94k þ 48 for integers k; green strands are lengths 31

and 21, so lane 4 has bands at 52k and 52k þ 21; blue strands are both length 47,

so lane 6 has bands at 94k and 94k þ 47; and yellow strands are lengths 21 and 31,

so lane 8 has bands at 52k and 52k þ 31.


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samples contain 2-D sheets many micrometres long, often more than200 nm wide (Fig. 3a, d). The apparent height of the sheets is1:4 6 0:5 nm, suggestive of a monolayer of DNA. The sheets oftenseem ripped and appear to have a grain, in that rips have a preferreddirection consistent with the design (Fig. 1c). In the DAO-E lattice, avertical rip requires breaking six sticky-end bonds per 12 nm torn,whereas a horizontal rip requires breaking only one sticky-end bondper 13 nm torn. A possible vertical column, perpendicular to therips, is indicated in Fig. 3a (arrows). Although in this image thecolumns are barely perceptible, Fourier analysis shows a peak at13 6 1 nm, suggesting that observed columns are 1 DX wide.Periodic topographic features would not be expected in the idealAB lattice; however, a vertically stretched lattice may have gapsbetween the DX units that could produce the periodic features seenhere. Because crystals are found in AFM samples taken from boththe top and the bottom of the solution, we believe that crystals formin solution and are not due to interaction with a surface.

Control of surface topographyThe self-assembling AB lattice can serve as scaffolding for other

molecular structures. We have decorated B with two DNA hairpinsequences inserted into its component strands, which we call B (Fig.1d). So decorated, the vertical columns of the lattice becomestrikingly apparent as stripes in AFM images (Fig. 3b, c, e, f),further confirming the proper self-assembly of the 2-D lattice. Thespacing of the decorated columns is 25 6 2 nm for the DAO-Elattice and 33 6 3 nm for the DAE-O lattice, indicating that everyother column is decorated, in accord with the design. Slow anneal-ing at 20 8C and gentle handling of the DAO-E sample duringdeposition and washing has produced single crystals measuring upto 2 3 8 mm (Fig. 4a–c). Close examination shows that the stripesare continuous across the crystal, and thus it appears to be a singledomain containing over 500,000 DX units.

Instead of DNA hairpins, other chemical groups can be used tolabel the DX molecules. Previously, biotin–streptavidin–gold hasbeen used to label linear DNA for imaging by AFM25,26. We have used1.4-nm nanogold–streptavidin conjugates to label DAE molecules.For these experiments, the central strand of B contains a 59 biotingroup; after assembly of AB lattices, the solution containing DNAlattices is incubated with streptavidin–nanogold conjugates and

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b

c f

e

da

Figure 3 AFM images of two-unit lattices. a, DAO-E AB lattice. A possible vertical

column is indicated by the arrows. Fourier analysis shows 13 6 1nm periodicity;

each DAO is 12.6 nm wide. b and c, DAO-E AB lattice (two views of the same

sample). Stripes have 25 6 2nm periodicity; the expected value is 25.2nm. d,

DAE-O AB lattice. e and f, DAE-O AB lattice (for different samples, see Methods).

Stripes have 33 6 3 nm periodicity; the expected value is 32 nm. All scale bars are

300 nm; images show 500 3 500nm or 1:5 3 1:5 mm. The grey scale indicates the

height above the mica surface; the apparent lattice height is between 1 and 2 nm.

a

b

f

e

d

c

Figure 4 AFM images showing large crystals and modifications of lattice

periodicity and surface features. a–c, DAO-E AB lattice at three levels of detail (all

the same sample). The largest domain is ,2 3 8 mm, and contains ,500,000 DX

units. d, DAE-O AB lattice in which B has been labelled with biotin–streptavidin–

nanogold. e and f, DAE-O ABCD lattice at two levels of detail (the same sample).

Stripes have 66 6 5nm periodicity; the expected value is 64nm. All scale bars are

300 nm; images show 500 3 500 nm, 1:5 3 1:5 mm, or 10 3 10 mm. The grey scale

indicates the height above the mica surface; the apparent lattice height is

between 1 and 2nm.


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then imaged by AFM (Fig. 4d). We have not confirmed that thenanogold particles remain conjugated to the streptavidin molecules;the surface topography may be due to streptavidin molecules alone.

We have also tested DAO and DAE systems incorporating onlyone of the two hairpins in B, DAO systems in which the 3-armjunctions are relocated by two nucleotides towards the centre of themolecule, and DAE systems in which the arms are one nucleotidelonger or shorter. All systems produced results similar to thoseshown in Fig. 3 when imaged by AFM (data not shown). The latticeassembly appears to be robust to variations in the local DX structureand is not sensitive to small variations in the annealing protocol.(The results reported here were obtained in two laboratories usingdifferent buffers, annealing conditions, and AFM instruments.)

Choice of sticky ends predictably determines the associationsbetween DX units. Therefore it is straightforward to modify the ABsystem into a 4-DX system with twice the period (Fig. 1a, right).This requires the use of twice as many unique sticky-end sequencesto control the unique association of DX units A, B, C, and D. Wehave created such a system in the DAE-O topology, where a singleunit, D, is decorated with two hairpins. Crystals in this system showstripes spaced every 66 6 5 nm, confirming that every fourthvertical column is decorated (Fig. 4e, f).

In all images of AB, AB and ABCD systems, we observed manyDNA structures in addition to the isolated 2-D crystals discussedabove. In many images, the 2-D crystals appear to overlap, leadingto discrete steps in thickness (Figs 3c, 4a, d). The arrangementof crystals on the mica—solitary, overlapping, piled up like drift-wood, ripped to shreds—depends sensitively upon DNA concen-tration and upon the sample preparation procedure, especially thewash step. Prominently, the background of every image containssmall objects, which we assume to be associations of small numbersof DX units. Also, long, thin ‘rods’ appear in some prepara-tions (Figs 3f, 4d, lower right). These structures have not beencharacterized.

ApplicationsSelf-assembly is increasingly becoming recognized as a route tonanotechnology27. Our results demonstrate the potential of usingDNA to create self-assembling periodic nanostructures. The periodicblocks used here are composed of either two or four individual DXunits. However, the number of component tiles in the repeat unitdoes not appear to be limited to such small numbers, suggestingthat complex patterns could be assembled into periodic arrays.These patterns could be either direct targets in nanofabrication oraids to the construction of such targets. Because oligonucleotidesynthesis can readily incorporate modified bases at arbitrary posi-tions, it should be possible to control the structure within theperiodic block by decoration with chemical groups, catalysts,enzymes and other proteins28, metallic nanoclusters29,30, conductingsilver clusters31, DNA enzymes32, or other DNA nanostructures suchas polyhedra33,34.

It may be possible to extend the two-dimensional lattices demon-strated here into three dimensions. Designed crystals could serve asscaffolds for the crystallization of macromolecules2, as photonicmaterials with novel properties35, as designable zeolite-like materialsfor use as catalysts or as molecular sieves36, and as scaffolds for theassembly of molecular electronic components37 or biochips38.

The self-assembly of aperiodic structures should also be consid-ered. It may be possible to design molecular Wang tiles that self-assemble into aperiodic crystals according to algorithmic rules10,14.It will be crucial to understand the mechanisms of crystallogenesisand crystal growth in this system to provide a firm underpinning fortheoretical proposals of computation by self-assembly.

Progress in this field will require detailed knowledge of thephysical, kinetic, structural, dynamic and thermodynamic para-meters that characterize DNA self-assembly. Additionally, improvedmethods for error reduction and purification must be developed.

The approach described here provides a uniquely versatile experi-mental system for investigating these issues. M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Methods

DNA sequences and synthesis. Figure 1d shows sequences used in theseexperiments; for historical reasons, some figures show experiments wherevariants of these sequences were used. The sequences for DAO-E A, B, and Bgiven in Fig. 1d were used for Fig. 3b, c. Figures 3a, 4a–c, show DAO systemswith symmetrical sticky ends: the sequence for the green strands of DAO A is59TCACT…GAGAT39 and the sequence for the blue strands of DAO B and B is59AGTGA…ATCTC39. The sequences for the DAE-O A and B units used inFig. 3d are modified from those given in Fig. 1d by deletion of the rightmost A⋅Tbase pair in the upper helix of A, addition of C to the upper-rightmost 59 end ofA, and deletion of C from the lower-leftmost 39 end of B; also the central strandof A is cyclically permuted to begin 59GCATGT…and the central strand of B iscyclically permuted to begin 59GGTCAC…. For Fig. 3e, the sequences for theDAE-O A are as shown in Fig. 1d, but both hairpins of B stem from the lowerhelix; thus the upper strand is as in B, and the central strand is 59ACTGGTTAGTGGATTGCGTAGGCGAGTAGTTTTCTACTCGCTTTACAACGCCACCGATGCGGTC39. The sequences for the DAE-O A and B units used in Fig. 3f areexactly as shown in Fig. 1d. Sequences for ABCD are available as SupplementaryInformation. All oligonucleotides were synthesized by standard methods,PAGE purified, and quantitated by ultraviolet absorption at 260 nm in H2O.Annealing of oligonucleotides. The strands of each DX unit were mixedstoichiometrically and dissolved to 0.2–2 mM in TAE/Mg2+ buffer (40 mMTris-HCl (pH 8.0), 1 mM EDTA, 3 mM Na+, 12.5 mM Mg2+) or in a HEPESbuffer (10 mM HEPES, 6 mM MgCl2, 1 mM EDTA, pH 7.8). The solutions wereannealed from 90 8C to room temperature over the course of several hours in aPerkin-Elmer polymerase chain reaction (PCR) machine (to preventconcentration by evaporation) or were annealed from 100 8C to roomtemperature during 40 h in a 2-litre water bath insulated in a styrofoam box.To produce lattices, equal amounts of each DX were mixed and annealed from50 8C to 20 8C for up to 36 h. In some cases (Fig. 3a–c), all strands were mixedtogether from the start.Gel electrophoresis. For gel-based studies, T4 polynucleotide kinase(Amersham) was used to phosphorylate strands with 32P; these strands werethen PAGE-purified and mixed with an excess of unlabelled strands. Non-denaturing 4, 5, or 8% PAGE (19:1 acrylamide:bisacrylamide) in TAE/Mg2+ wasdone at 4 8C or at room temperature. For denaturing experiments, afterannealing in T4 DNA ligase buffer (Amersham) (66 mM Tris-HCl (pH 7.6),6.6 mM MgCl2, 10 mM DTT, 66 mM ATP), 1 ml containing 10 units of T4 DNAligase (Amersham) was added to 10 ml DNA solution and incubated for up to24 h at 16 8C or at room temperature. For exonuclease reactions, 50 units ofexonuclease III (Amersham) and 5 units of exonuclease I (Amersham) wereadded after ligation and incubated an additional 3.5 h at 37 8C. The solutionwas added to an excess of denaturing dye buffer (0.1% xylene cyanol FFtracking dye in 90% formamide with 1 mM EDTA, 10 mM NaOH) and heatedto 90 8C for at least 5 min before loading. Denaturing gels contained 4%acrylamide (90:1 acrylamide:bisacrylamide) and 8.3 M urea in TBE (89 mMTris-HCl (pH 8.0), 89 mM boric acid, 2 mM EDTA). Gels were analysed byusing a Phosphorimager.Labelling with biotin–streptavidin–nanogold. The central strand of DAE-OB was synthesized containing a 59 biotin group. Lattices were formed by annealingas described. After annealing, a stoichiometric amount of streptavidin–nanogold(1.4 nm; Nanoprobe) in a buffer provided by the supplier (20 mM phosphate,150 mM NaCl (pH 7.4), 0.1% BSA, 0.05% NaN3) was added, so that the molarratio of biotin to streptavidin was 1:1. The solution was left at roomtemperature for 1 h and then imaged by AFM as described below.Preparation of AFM sample. 2–10 ml were spotted onto freshly cleaved mica(Ted Pella) and left to adsorb to the surface for 2 min. To remove buffer salts, 5–10 drops of doubly distilled or nanopure H2O were placed on the mica, the dropwas shaken off and the sample was dried with compressed air. Imaging wasdone under isopropanol in a fluid cell on a NanoScope II using the D or Escanner and commercial 200-mm cantilevers with Si3N4 tips (DigitalInstruments). The feedback setpoint was adjusted frequently to minimizecontact force to ,1 to 5 nN. Images were processed with a first- or third-order‘flatten filter’, which independently subtracts a first- or third-order polynomial

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fit from each scanline to remove tip artefacts; however, this technique canintroduce false ‘shadows’.

Received 10 March; accepted 5 May 1998.

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Supplementary information is available on Nature’s World-Wide Web site (http://www.nature.com) oras paper copy from the London editorial office of Nature.

Acknowledgements. We thank J. Hopfield, S. Roweis, S. Mahajan, C. Brody, L. Adleman and P.Rothemund for discussion; J. Abelson and his group for use of his laboratory and for technical advice;A. Segal, E. Rabani and R. Moision for instruction and advice on AFM imaging; the Beckman InstituteMolecular Materials Resource Center for assistance and use of their AFM facilities; F. Furuya for help withlabelling; and M. Yoder, V. Morozov, D. Stokes, M. Simon and J. Wall for assistance in early attempts tovisualize DNA lattices. The research at Caltech has been supported by the National Institute for MentalHealth, General Motors’ Technology Research Partnerships program, and by the Center for Neuro-morphic Systems Engineering as a part of the NSF Engineering Research Center Program. The research atNYU has been supported by the Office of Naval Research, the National Institute of General MedicalSciences, and the NSF.

Correspondence and requests for materials should be addressed to E.W. (e-mail: [email protected]) or N.C.S. (e-mail: [email protected]).

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